It's extremely rare for the surviving members of the Beatles to perform together, but this month they found a cause they could both believe in - and it wasn't cold, hard cash. Paul McCartney and Ringo Starr took to a New York stage with other top musicians, including Moby and Sheryl Crow, for a one-off concert entitled Change Begins Within. All the profits - around $3m (£2m) - were earmarked for the David Lynch Foundation, an organisation headed by the famously esoteric film director which plans to teach Transcendental Meditation (TM) to a million young people in the US.

"Over 40 years ago, we ended up in Rishikesh," said Starr, "where we hung out with Maharishi ... Since then - sometimes a lot, sometimes a little - I have meditated."

Now Lynch plans to give the gift of meditation to as many schoolchildren as possible. In 2005, the TM programme run by the Maharishi Foundation, in partnership with Lynch's foundation, set up the US Committee for Stress-Free Schools. This aims to encourage ordinary schools to incorporate TM into their day; it has been suggested that this can both boost creativity and academic achievement, and tackle problems including attention deficit hyperactivity disorder (ADHD), depression, stress and substance abuse.

It all sounds very positive, but the idea of introducing TM into schools is not without controversy. Indeed, for many people it can seem like a kooky child-rearing idea too far. There are questions about whether it is appropriate for children - indeed, whether children can master a practice that involves extended bouts of concentration. Edzard Ernst, professor of complementary medicine at the Peninsula Medical School in Exeter, says that "there is no good evidence that TM has positive effects on children. The data that exist are all deeply flawed."

Some vocal critics in the US have also called TM a "stealth religion", suggesting that it is rooted in Hinduism and that introducing it into the school system therefore violates church-state separation. In 2006, when the David Lynch Foundation awarded a grant to Terra Linda high school in California, outraged parents compared TM to a cult. One Californian religious group threatened to sue.

Supporters of Transcendental Meditation refute these allegations, and point out that the practice pre-dates Hinduism by 5,000 years. They say that it is not a religion or a philosophy; nor does it, as popular mythology suggests, require growing a beard and levitating on a carpet. It is merely a practical brain-calming technique that involves repeating a sound, or mantra.

Lynch himself is Presbyterian, and on his foundation's website he writes that he has "been 'diving within' ... for over 30 years. It has changed my life, my world." In his book, Catching the Big Fish: Meditation, Consciousness and Creativity, he describes how daily TM allows him to tap into his creativity, find inspiration, and bring all manner of projects to fruition. Now he feels he must pass this on in order to "save the next generation".

Norma Sullivan, spokesperson for TM in the UK, says that children as young as five can manage the technique. "At this age they are too young to sit with their eyes closed," she says. "But they can learn the TM 'walking technique' - a simple form of meditation involving the repetition of a sound." At the age of 10, a child can graduate to the "sitting technique" where they are taught to repeat a mantra while seated with eyes closed.

After each session, says Sullivan, children "feel more relaxed, happier and think more clearly".

Someone who has committed to the practice wholeheartedly is Freddy Fuller, 16, who meditates for 45 minutes, morning and evening, plus two 15-minute sessions during the school day. "Lots of people think it's really weird," he says, "but it definitely helps all sorts of areas of my life. If I'm feeling stressed, I meditate and it calms me. It helps me to focus on schoolwork. I recently had lots of homework and my thoughts were all over the place. I meditated, then sat down and could think really clearly." The daily two-hour commitment may sound huge, but, he says, "It's surprisingly easy. I will try to do it for ever."

Fuller attends the Maharishi School of the Age of Enlightenment, in Skelmersdale, Lancashire. This is a non-academically selective private school with 70 pupils, aged four to 16, all of whom begin and end each day with 10 minutes or more of silent meditation. It is the only Maharishi school in Britain (although Sullivan says that three secondary schools in the UK have integrated TM into their daily routine). The children follow a normal curriculum, says head teacher Derek Cassells, but teachers use specific TM techniques to encourage them to appreciate "the harmony underlying the diversity of existence".

The school's GCSE results are twice the national average - which could, of course, be attributed to the fact that it is a very small, nurturing private school. However, Cassells points out that in the US some tough high schools have taken on TM techniques with impressive results, both academically and behaviourally.

There's no doubt that stress can interfere with children's attention, memory and organisation skills - and a recent national inquiry by the Children's Society portrayed Britain as a nation of pressurised and overtested children. So, given all the evidence, should we replace our school assemblies with silent meditation?

Educational psychologist Kairen Cullen, associate fellow of the British Psychological Society, sounds a note of caution. She questions "at what age you could realistically expect a child to engage with this. It would certainly take discipline and require physical and mental control and focus." She does believe that TM can, in general, be a helpful tool, but is "not aware of any empirical research specifically showing the benefits to children. This is a very difficult sample group to access and it would be very hard to provide empirical evidence - any claims would therefore be pretty speculative."

Perhaps the biggest obstacle, she says, would be getting children to engage with TM in the first place. "Just adding a few classes to the curriculum would be cosmetic," she says. "This is an entire lifestyle package and, for children in today's fast-paced society, that would be quite a culture clash."

Phillip Hodson, fellow of the British Association for Counselling and Psychotherapy, believes that regular meditation could boost children's wellbeing. "Thoughts are psychoactive - as powerful as drugs," he says. "Anything that encourages a child's emotional intelligence would be a positive antidote to our goal-orientated education system. It could also be very useful to give children techniques that they can use in moments of stress."

Hodson doesn't subscribe solely to TM, however, saying that it "is just one of a range of relaxation techniques that can help children - the simplest being controlled breathing". And it is potentially problematic to rely on one form of meditation. "I would query any grand claims that a single technique can change your entire life," he says. "If it could, wouldn't we all be doing it?"

Lynch certainly believes that we should and at times his argument does seem persuasive. "Every child should have one class period a day to dive within himself and experience the field of silence - bliss - the enormous reservoir of energy and intelligence that is deep within all of us," he writes. But whether this really could save the next generation remains to be seen.